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Millimeter Wave RADAR Power-Range Spectra Interpretation 51

2.4.2.1 Thermal noise
Thermal noise is generated in the RADAR receiver electronics. The noise power
is given by P N (in Watts), where

P N = kT 0 β (2.8)

where k is the Boltzmann constant, T 0 is the temperature, and β is the receiver
bandwidth [22]. As shown in Section 2.3, the power in the beat frequency
signal (found from the FFT of this signal) is affected by the thermal noise power

a R (t−τ), which contributesto A in Equation(2.6). Itcan beshown by analyzing
the transition of this thermal (Gaussian) noise through the entire FMCW range
detection process that when a target is present (strong received signal) the noise
in the power–range spectrum follows a Gaussian distribution. When no target
is present (weak or no reflected signal) it will be demonstrated from the results
that the noise power follows a Weibull distribution. Therefore measurements
with target presence/absence were made to verify these distributions and to
quantify the power variance during target absence/presence.

2.4.2.2 Phase noise
Another source of noise which affects the range spectra is the phase noise. The
phase noise is generated by the frequency instability of the oscillator due to
the thermal noise. Ideally for a particular input voltage to the VCO, the output
has a single spectral component. In reality, the VCO generates a spectrum
of frequencies with finite bandwidth which constitutes phase noise. This is
shown in Equation (2.6), where a band of noise frequencies with different phase
components, φ(t, τ) affects the desired signal frequency, which corresponds
to range. The phase noise broadens the received power peaks and reduces the
sensitivity of range detection [11] as shown in Figure 2.4. 3 This introduces
noise into the range estimate itself. Experimental data provides insight into the
phase noise distribution. For predicting the RADAR range spectra, the peaks at
predicted targets are broadened by a small constant amount. This broadening
4
is based on real measurements, which have shown the peaks to have widths
ranging from 2.5 to 3.5 m. This has been observed from targets, of different
RCS, placed at different distances from the RADAR.
Figure 2.5 shows 1000 superimposed range bins obtained for the same
RADAR swash plate bearing angle. Figure 2.5a shows the entire range bins
over the full 200 m range, while Figure 2.5b shows a zoomed view of the
spectra obtained from the feature at 10.25 m. From the figures, it is evident that
3 The peaks and skirts shown in Figure 2.4 occur due to the leakage of signals from the transmitter
into the mixer through the circulator and also due to the antenna impedance mismatch [11].
4 At their intersections with the high pass filter gain curve shown in Figure 2.3.

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c002” — 2006/3/31 — 17:29 — page 51 — #11